Medical Sciences: cram pack

Formula sheets, the key method steps for every topic and 14 practice problems, with full solutions at the back.

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1Formulas and methods

Arterial blood gas interpretation

Normal ranges
pH 7.35–7.45, PaCO₂ 35–45 mmHg (4.7–6.0 kPa), HCO₃⁻ 22–26 mmol/L
ROME
Respiratory: PaCO₂ opposite to pH; Metabolic: HCO₃⁻ equal to pH
Winter’s formula
PaCO₂ = 1.5·HCO₃⁻ + 8 ± 2
Metabolic alkalosis
PaCO₂ ≈ 0.7·HCO₃⁻ + 21
Anion gap
AG = Na⁺ − (Cl⁻ + HCO₃⁻) ≈ 8–12
Albumin-corrected gap
AG + 2.5·(4.0 − alb g/dL) = AG + 0.25·(40 − alb g/L)
Delta ratio
(AG − 12)/(24 − HCO₃⁻)
P/F ratio
PaO₂/FiO₂
Alveolar gas equation
PAO₂ = FiO₂·(760 − 47) − PaCO₂/0.8
Serum osmolality
2·Na⁺ + glucose + urea (2·Na⁺ + glucose/18 + BUN/2.8)

Method

  1. Read the pH: below 7.35 is acidosis, above 7.45 alkalosis.
  2. Find the value that explains it: PaCO₂ moving opposite to the pH is respiratory, HCO₃⁻ moving with the pH is metabolic.
  3. Look at the other value: normal means uncompensated, abnormal in the compensating direction means partial compensation, and a normal pH with both abnormal means full compensation.
  4. In a metabolic acidosis, compare PaCO₂ with Winter’s formula, 1.5·HCO₃⁻ + 8 ± 2, and calculate the anion gap Na⁺ − (Cl⁻ + HCO₃⁻).
  5. Check a high anion gap with the delta ratio and, when albumin is low, with the corrected gap.

ECG rhythm strip interpretation

Paper (25 mm/s, 10 mm/mV)
1 small box = 0.04 s, 1 large box = 0.20 s, 10 mm = 1 mV
Heart rate, regular rhythm
300 ÷ large boxes = 1500 ÷ small boxes = 60 ÷ RR (s)
Heart rate, irregular rhythm
QRS complexes in 6 s × 10
Normal PR interval
0.12–0.20 s
Normal QRS duration
< 0.12 s
QTc (Bazett)
QT/√RR
QTc (Fridericia)
QT/∛RR
QTc (Framingham)
QT + 154·(1 − RR)
Sinus rates
bradycardia < 60, normal 60–100, tachycardia > 100 /min
Escape rates
junctional 40–60, ventricular 20–40 /min
Fast rhythms
SVT 150–250 /min (narrow), VT > 100 /min (wide)

Method

  1. Rate: for a regular rhythm divide 300 by the large boxes or 1500 by the small boxes between two R waves; for an irregular rhythm count the QRS complexes in 6 seconds and multiply by 10.
  2. Rhythm: compare the R–R intervals. Equal is regular; a repeating pattern is regularly irregular; no pattern at all is irregularly irregular.
  3. P waves: is there an upright P wave in lead II before every QRS, all alike? Look for fibrillatory or sawtooth waves, inverted P waves and P waves without a QRS.
  4. PR interval: from the start of P to the start of the QRS, normally 0.12–0.20 s and constant. Watch whether it lengthens, stays fixed before a dropped beat, or varies at random.
  5. QRS duration: below 0.12 s is narrow; 0.12 s or more is wide. Then name the rhythm, and for the QT use QTc = QT/√RR (Bazett) with times in seconds.

Evidence-based practice statistics

Sensitivity and specificity
Se = a/(a + c), Sp = d/(b + d)
Predictive values
PPV = a/(a + b), NPV = d/(c + d)
Accuracy
(a + d)/n
Likelihood ratios
LR+ = Se/(1 − Sp), LR− = (1 − Se)/Sp
PPV at prevalence p
Se·p / (Se·p + (1 − Sp)(1 − p))
Odds
odds = p/(1 − p); p = odds/(1 + odds); post-test odds = pre-test odds × LR
Risk measures
RR = EER/CER, ARR = CER − EER, RRR = ARR/CER
Number needed to treat
NNT = 1/ARR, rounded up; NNH = 1/(EER − CER)
Odds ratio
OR = ad/(bc)
Incidence rate
new cases / person-time

Method

  1. Draw the 2 × 2 table and label a, b, c and d before you calculate.
  2. Read sensitivity and specificity down the columns, predictive values along the rows.
  3. For another prevalence, imagine 10 000 people and fill the table with Se, Sp and the prevalence.
  4. For a likelihood ratio, convert the probability to odds, multiply, and convert back.
  5. For a trial, find EER and CER first; then RR = EER/CER, ARR = CER − EER and NNT = 1/ARR rounded up.

2Practice problems

1.Human anatomyMedium

Which superficial vein in the front of the elbow is most often used for venepuncture?

  1. AGreat saphenous vein
  2. BBrachial vein
  3. CMedian cubital vein
  4. DAxillary vein
2.Human anatomyHard

Which structure is found in the posterior mediastinum?

  1. AThymus
  2. BOesophagus
  3. CAscending aorta
  4. DHeart
3.Human physiologyMedium

Which hormone increases water reabsorption in the collecting ducts of the kidney?

  1. AParathyroid hormone
  2. BAtrial natriuretic peptide
  3. CAldosterone
  4. DAntidiuretic hormone (ADH)
4.Human physiologyHard

Why does fetal haemoglobin have a higher affinity for oxygen than adult haemoglobin?

  1. AIt contains more iron per haem
  2. BIt has five subunits instead of four
  3. CFetal blood has a higher pH
  4. DIt binds 2,3-BPG less strongly
5.MicrobiologyMedium

Which part of the immune system produces antibodies?

  1. ACytotoxic T cells activated in the lymph nodes
  2. BNatural killer cells
  3. CNeutrophils
  4. DPlasma cells derived from B lymphocytes
6.MicrobiologyHard

A healthcare worker's blood test is positive for anti-HBs (hepatitis B surface antibody) and negative for HBsAg and anti-HBc. What does this most likely mean?

  1. ACurrent acute hepatitis B infection
  2. BPast natural infection that has cleared
  3. CChronic hepatitis B infection
  4. DImmunity from hepatitis B vaccination
7.PharmacologyMedium

Which side effects are most common when starting gabapentin?

  1. ACough and runny nose
  2. BInsomnia and agitation
  3. CHair loss and weight loss
  4. DDrowsiness and dizziness
8.PharmacologyHard

A patient took a large paracetamol (acetaminophen) overdose 6 hours ago and feels well. Why is treatment still urgent?

  1. AThe drug will cause kidney stones within a few hours
  2. BParacetamol overdose only causes harm if symptoms start in the first hour
  3. CThe patient is at risk of immediate respiratory arrest
  4. DLiver damage appears 1–3 days later, and early treatment works best
9.Arterial blood gas interpretationMedium

Practice values: Na⁺ 152 mmol/L, glucose 11.5 mmol/L and urea 24.5 mmol/L. Calculate the serum osmolality Osm = 2·Na⁺ + glucose + urea to the nearest whole number.

Na⁺ 152 mmol/Lglucose 11.5 mmol/Lurea 24.5 mmol/L
Osm = mOsm/kg
10.Arterial blood gas interpretationHard
pH7.357.457.17PaCO₂mmHg354579HCO₃⁻mmol/L222628acutechronicacute on chronic

A practice gas shows a respiratory acidosis: pH 7.17, PaCO₂ 79 mmHg (10.5 kPa), HCO₃⁻ 28 mmol/L. Use the rules ‘HCO₃⁻ rises 1 mmol/L per 10 mmHg (acute) or 3.5 mmol/L per 10 mmHg (chronic)’ to classify it. Click your answer.

pH 7.17PaCO₂ 79 mmHg (10.5 kPa)HCO₃⁻ 28 mmol/L
  1. 1acute
  2. 2chronic
  3. 3acute on chronic
11.ECG rhythm strip interpretationMedium
II25 mm/s · 10 mm/mVfirst-degree AV blocknormal sinus rhythmatrial fibrillationsinus rhythm with PVCs

Interpret this lead II rhythm strip. Which rhythm is it? Click your answer.

lead II, 25 mm/s, 10 mm/mV1 small box = 0.04 s, 1 large box = 0.20 sstrip length 6 s
  1. 1first-degree AV block
  2. 2normal sinus rhythm
  3. 3atrial fibrillation
  4. 4sinus rhythm with PVCs
12.ECG rhythm strip interpretationHard
II25 mm/s · 10 mm/mVsecond-degree AV block type IIthird-degree (complete) AV blockfirst-degree AV blocksecond-degree AV block type I (Wenckebach)

This lead II strip shows a conduction problem between the atria and the ventricles. Which rhythm is it? Click your answer.

lead II, 25 mm/s, 10 mm/mV1 small box = 0.04 s, 1 large box = 0.20 sstrip length 6 s
  1. 1second-degree AV block type II
  2. 2third-degree (complete) AV block
  3. 3first-degree AV block
  4. 4second-degree AV block type I (Wenckebach)
13.Evidence-based practice statisticsMedium
eventno eventtotaltreatment20100120abcontrol149471620cd

Practice exercise (made-up values, not clinical guidance). In a randomised trial, 120 patients received a new treatment and 620 received the control treatment. The table shows how many in each group had the outcome (an unwanted event such as a stroke). Find the relative risk reduction RRR as a percentage. Round to one decimal place.

treatment: 20/120control: 149/620
RRR = %
14.Evidence-based practice statisticsHard
p (%)PPV (%)2%PPV = ?100

Practice exercise (made-up values, not clinical guidance). A screening test has a sensitivity of 83% and a specificity of 94%. It is used in a population where the prevalence is 2%. Find the positive predictive value PPV as a percentage. Round to one decimal place.

Se = 83%Sp = 94%p = 2%
PPV = %

3Solutions

1.Human anatomy

Answer: C · Median cubital vein

Why this is the answer

The median cubital vein crosses the cubital fossa between the cephalic and basilic veins. It is superficial, large and fairly fixed, so it is easy to puncture.

Answer

C · Median cubital vein
2.Human anatomy

Answer: B · Oesophagus

Why this is the answer

The posterior mediastinum contains the oesophagus, descending aorta, azygos veins and thoracic duct. The heart and ascending aorta are in the middle mediastinum; the thymus is in the superior and anterior mediastinum.

Answer

B · Oesophagus
3.Human physiology

Answer: D · Antidiuretic hormone (ADH)

Why this is the answer

ADH (vasopressin) from the posterior pituitary inserts aquaporin-2 channels, making the collecting duct permeable to water and concentrating the urine.

Answer

D · Antidiuretic hormone (ADH)
4.Human physiology

Answer: D · It binds 2,3-BPG less strongly

Why this is the answer

The gamma chains of HbF bind 2,3-BPG poorly, so the curve is shifted left. This lets fetal blood take oxygen from maternal blood in the placenta.

Answer

D · It binds 2,3-BPG less strongly
5.Microbiology

Answer: D · Plasma cells derived from B lymphocytes

Why this is the answer

Activated B cells differentiate into plasma cells, which secrete antibodies. Cytotoxic T cells and NK cells kill infected cells directly.

Answer

D · Plasma cells derived from B lymphocytes
6.Microbiology

Answer: D · Immunity from hepatitis B vaccination

Why this is the answer

The vaccine contains HBsAg, so a vaccinated person makes anti-HBs but no anti-HBc. Past natural infection gives both anti-HBs and anti-HBc, and ongoing infection shows HBsAg.

Answer

D · Immunity from hepatitis B vaccination
7.Pharmacology

Answer: D · Drowsiness and dizziness

Why this is the answer

Gabapentin and pregabalin commonly cause sedation, dizziness and unsteadiness, which raise the risk of falls. They also increase sedation when combined with opioids.

Answer

D · Drowsiness and dizziness
8.Pharmacology

Answer: D · Liver damage appears 1–3 days later, and early treatment works best

Why this is the answer

Paracetamol overdose often causes few symptoms at first, while the toxic metabolite damages the liver. Liver injury peaks after about 3 days, so the decision to treat is based on the timed blood level, not on symptoms.

Answer

D · Liver damage appears 1–3 days later, and early treatment works best
9.Arterial blood gas interpretation

Answer: Osm = 340 mOsm/kg

Derived values: calculated serum osmolality is 2·Na⁺ + glucose + urea with all values in mmol/L (2·Na⁺ + glucose/18 + BUN/2.8 with glucose and BUN in mg/dL); normal is about 275–295 mOsm/kg. The P/F ratio is PaO₂ divided by FiO₂ as a fraction. The alveolar oxygen pressure is PAO₂ = FiO₂·(760 − 47) − PaCO₂/0.8 mmHg at sea level, and the A–a gradient is PAO₂ − PaO₂.

Calculated osmolality

Osm = 2·152 + 11.5 + 24.5 = 340 ≈ 340 mOsm/kg

Answer

Osm = 340 mOsm/kg
10.Arterial blood gas interpretation

Answer: acute

Expected compensation: in metabolic acidosis Winter’s formula predicts PaCO₂ = 1.5·HCO₃⁻ + 8 ± 2 mmHg; a measured value above that range points to an additional respiratory acidosis, below it to an additional respiratory alkalosis. The anion gap AG = Na⁺ − (Cl⁻ + HCO₃⁻), normally about 8–12 mmol/L, separates high-gap from normal-gap metabolic acidosis; low albumin hides a high gap (add 2.5 per g/dL that albumin is below 4.0). The delta ratio (AG − 12)/(24 − HCO₃⁻) between about 0.8 and 2 fits a pure high-gap acidosis (some texts use 1 instead of 0.8), below that an added normal-gap acidosis, and above 2 an added metabolic alkalosis.

Expected HCO₃⁻

acute: 24 + 1·3.9 = 27.9 mmol/L
chronic: 24 + 3.5·3.9 = 37.65 mmol/L

Compare

measured: 28 mmol/L → acute

Answer

acute
11.ECG rhythm strip interpretation

Answer: sinus rhythm with PVCs

Rhythm criteria (lead II): sinus rhythm has an upright P wave before every QRS, a constant PR of 0.12–0.20 s and a narrow QRS: normal sinus rhythm at 60–100/min, sinus bradycardia below 60, sinus tachycardia above 100. Atrial fibrillation: no P waves, a fibrillatory baseline and an irregularly irregular R–R. Atrial flutter: sawtooth flutter waves at about 250–350/min with a fixed conduction ratio such as 2:1 or 4:1. First-degree AV block: sinus rhythm with a constant PR above 0.20 s. Junctional rhythm: narrow QRS at 40–60/min with absent or inverted P waves (PR below 0.12 s, or P after the QRS). A PVC is an early, wide (0.12 s or more), bizarre QRS without a P wave, with the T wave in the opposite direction and usually a full compensatory pause; in bigeminy every second beat is a PVC.

Five steps

1. Rate: 8 QRS complexes in 6 s, × 10 = 80 per minute.
2. Rhythm: regular (0.76 s) except for the early beats and the pause after each of them.
3. P waves: upright before every narrow QRS; none before the early wide beats.
4. PR interval: 0.18 s, constant, within 0.12–0.20 s.
5. QRS: 0.08 s in the sinus beats; the early beats are wide (0.14 s) and bizarre, with the T wave pointing the other way.

Interpretation

sinus rhythm with PVCs

Answer

sinus rhythm with PVCs
12.ECG rhythm strip interpretation

Answer: second-degree AV block type II

AV blocks: march out the P waves and check which ones are followed by a QRS. First-degree: every P conducted, PR constant and above 0.20 s. Second-degree type I (Mobitz I, Wenckebach): the PR lengthens from beat to beat until one P wave is not conducted, then the cycle starts again (group beating). Second-degree type II (Mobitz II): the PR of the conducted beats stays constant, and P waves are suddenly not conducted; the QRS is often wide. Third-degree (complete) block: P waves and QRS complexes are each regular but independent, the PR varies at random and the atrial rate is faster than the escape rate (junctional 40–60/min with a narrow QRS, ventricular 20–40/min with a wide QRS). A 2:1 block cannot be called type I or type II from one strip.

Five steps

1. Rate: 5 QRS complexes in 6 s, × 10 = 50 per minute.
2. Rhythm: the P waves are regular; R–R is regular except for a long pause where a QRS is missing.
3. P waves: upright and regular (P–P 0.92 s, 65 per minute); one P in every 4 is not followed by a QRS.
4. PR interval: constant at 0.16 s in the conducted beats.
5. QRS: 0.08 s, narrow (below 0.12 s).

Interpretation

second-degree AV block type II

Answer

second-degree AV block type II

Type II and third-degree blocks are the ones that can suddenly progress, so textbooks rank them as more serious than type I.

13.Evidence-based practice statistics

Answer: RRR = 30.6 %

Likelihood ratios and risk measures: LR+ = sensitivity/(1 − specificity), LR− = (1 − sensitivity)/specificity. In a trial, EER and CER are the event rates with and without treatment: RR = EER/CER, ARR = CER − EER, RRR = ARR/CER and NNT = 1/ARR, rounded up. In a case-control study only the odds ratio OR = ad/(bc) can be used. An incidence rate = new cases/person-time.

Event rates

EER = 20/120 = 0.1667
CER = 149/620 = 0.2403

Relative risk reduction

ARR = 0.2403 − 0.1667 = 0.07366
RRR = 0.07366/0.2403 = 0.3065 ≈ 30.6%

Answer

RRR = 30.6%
14.Evidence-based practice statistics

Answer: PPV = 22 %

Predictive values depend on prevalence: PPV = Se·p/(Se·p + (1 − Sp)(1 − p)) and NPV = Sp(1 − p)/(Sp(1 − p) + (1 − Se)p). With likelihood ratios: pre-test odds = p/(1 − p), post-test odds = pre-test odds × LR, probability = odds/(1 + odds). For a population of N, true positives = N·p·Se and false positives = N·(1 − p)·(1 − Sp). NNT = 1/(CER × RRR), rounded up.

True and false positives (per person)

Se·p = 0.83·0.02 = 0.0166
(1 − Sp)·(1 − p) = 0.06·0.98 = 0.0588

Positive predictive value

PPV = 0.0166/(0.0166 + 0.0588) = 0.2202 ≈ 22%

Answer

PPV = 22%

The lower the prevalence, the lower the PPV of the same test.

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